Certain Integral Transforms of Generalized k-Bessel Function
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摘要
The objective of this note is to provide some(potentially useful) integral transforms(for example, Euler, Laplace, Whittaker etc.) associated with the generalized k-Bessel function defined by Saiful and Nisar [3]. We have also discussed some other transforms as special cases of our main results.
The objective of this note is to provide some(potentially useful) integral transforms(for example, Euler, Laplace, Whittaker etc.) associated with the generalized k-Bessel function defined by Saiful and Nisar [3]. We have also discussed some other transforms as special cases of our main results.
The objective of this note is to provide some(potentially useful) integral transforms(for example, Euler, Laplace, Whittaker etc.) associated with the generalized k-Bessel function defined by Saiful and Nisar [3]. We have also discussed some other transforms as special cases of our main results.
引文
[1] R. D′?az and E. Pariguan, On hypergeometric functions and k-Pochhammer symbol, Divulg.Mat., 15(2)(2007), 179–192.
[2] K. S. Gehlot, Differential equation of K-Bessel’s function and its properties, Nonlinear Analysis and Differential Equations, 2(2)(2014), 61–67.
[3] S. R. Mondal and K. S. Nisar, Certain unified integral formulas involving the generalized modified k-Bessel function of first kind, Commun. Korean Math. Soc., 32(2017), 47–53.
[4] G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press,Cambridge, 1992.
[5] K. S. Gehlot and S. D. Purohit, Fractional calculus of K-Bessel’s function, Acta Universitatis Apulensis, 38(2014), 273–278.
[6] E. D. Rainville, Special Functions, Macmillan, New York, 1960.
[7] C. Fox, The asymptotic expansion of generalized hypergeometric functions, Proc. London.Math. Soc., 27(4)(1928), 389–400
[8] E. M. Wright, The asymptotic expansion of integral functions defined by Taylor series, Philos. Trans. Roy. Soc. London, Ser. A, 238(1940), 423–451.
[9] E. M. Wright, The asymptotic expansion of the generalized hypergeometric function, Proc.London Math. Soc., 46(2)(1940), 389–408.
[10] K. S. Gehlot and J. C. Prajapati, Fractional calculus of generalized K-wright function, Journal of Fractional Calculus and Applications, 4(2013), 283–289.
[11] Y. Luchko, H. Martinez and J. Trujillo, Fractional Fourier transform and some of its applications, Fractional Calculus and Applied Analysis, An International Journal for Theory and Applications, 11(4)(2008), 457–470.
[12] A. Erde′lyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Tables of Integral Transforms,Vol. 2, McGraw-Hill, New York-Toronto-London, 1954.
[13] A. M. Mathai and R. K. Saxena, The H-Function with Applications in Statistics and Other Disciplines, Wiley Eastern, New Delhi and Wiley Halsted, New York, 1978.
[14] A. M. Mathai, R. K. Saxena, and H. J. Haubold, The H-Function, Theory and Applications,Springer, New York, 2010.
[15] H. M. Srivastava, Some Fox-Wright generalized hypergeometric functions and associated families of convolution operators, Applicable Analysis and Discrete Mathematics, 1(2007),56–71.
[16] L. G. Romero, G. A.Dorrego and R. A. Cerutti, The k-Bessel function of first kind, International Mathematical forum, 38(7)(2012), 1859–1854.
[2] K. S. Gehlot, Differential equation of K-Bessel’s function and its properties, Nonlinear Analysis and Differential Equations, 2(2)(2014), 61–67.
[3] S. R. Mondal and K. S. Nisar, Certain unified integral formulas involving the generalized modified k-Bessel function of first kind, Commun. Korean Math. Soc., 32(2017), 47–53.
[4] G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press,Cambridge, 1992.
[5] K. S. Gehlot and S. D. Purohit, Fractional calculus of K-Bessel’s function, Acta Universitatis Apulensis, 38(2014), 273–278.
[6] E. D. Rainville, Special Functions, Macmillan, New York, 1960.
[7] C. Fox, The asymptotic expansion of generalized hypergeometric functions, Proc. London.Math. Soc., 27(4)(1928), 389–400
[8] E. M. Wright, The asymptotic expansion of integral functions defined by Taylor series, Philos. Trans. Roy. Soc. London, Ser. A, 238(1940), 423–451.
[9] E. M. Wright, The asymptotic expansion of the generalized hypergeometric function, Proc.London Math. Soc., 46(2)(1940), 389–408.
[10] K. S. Gehlot and J. C. Prajapati, Fractional calculus of generalized K-wright function, Journal of Fractional Calculus and Applications, 4(2013), 283–289.
[11] Y. Luchko, H. Martinez and J. Trujillo, Fractional Fourier transform and some of its applications, Fractional Calculus and Applied Analysis, An International Journal for Theory and Applications, 11(4)(2008), 457–470.
[12] A. Erde′lyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Tables of Integral Transforms,Vol. 2, McGraw-Hill, New York-Toronto-London, 1954.
[13] A. M. Mathai and R. K. Saxena, The H-Function with Applications in Statistics and Other Disciplines, Wiley Eastern, New Delhi and Wiley Halsted, New York, 1978.
[14] A. M. Mathai, R. K. Saxena, and H. J. Haubold, The H-Function, Theory and Applications,Springer, New York, 2010.
[15] H. M. Srivastava, Some Fox-Wright generalized hypergeometric functions and associated families of convolution operators, Applicable Analysis and Discrete Mathematics, 1(2007),56–71.
[16] L. G. Romero, G. A.Dorrego and R. A. Cerutti, The k-Bessel function of first kind, International Mathematical forum, 38(7)(2012), 1859–1854.